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Harvard and other top universities are grappling with the same problem many states and cities are confronting: how to pay for health benefits they have promised to retirees.

Harvard’s liability for medical coverage will approach $1 billion next year, exceeding the obligations of a mid-size city. And like many local governments, elite schools could face a host of difficult choices as they try to meet these obligations, from reneging on promised benefits and cutting spending to raising tuition.

“They’re going to have to get out of that business,’’ said Joseph Mercurio, executive vice president of Boston University, which does not have a retiree medical plan. “It’s just too expensive.’’

A Globe review of financial reports at numerous private and public schools showed that retiree health benefit liabilities, which have received relatively little public attention, are enormous. In fiscal 2010, Harvard University’s obligation for retiree medical benefits exceeded its pension obligations for the first time.

“Addressing post-retirement costs is something that large institutions, including universities like Harvard, will need to consider carefully in the coming years,’’ he said. Harvard is looking at strategies “that will meet the needs of our current and future retirees in the most effective manner, while also maintaining the university’s fiscal well-being.’’

Shore said the strategies are still under discussion.

Harvard’s medical coverage liability for 20,900 current and future retirees, about $812 million, is bigger than the City of Worcester’s ($765 million). With approximately a $763 million pension liability, Harvard has total retiree obligations that top $1.6 billion, or 5 percent of its assets.

And these expenses are rising at a time when Harvard, the nation’s wealthiest university, has tightened its belt, following steep losses in its endowment during the financial crisis. The university trimmed $31 million from salaries and wages in the 2010 fiscal year — about the same amount that its retiree medical and pension payouts rose last year, nearly $35 million.

The benefit problem at universities reflects soaring health care costs across the country. Private universities don’t face pressures from taxpayers the way states, towns, and cities do, but they have to manage their expenses and explain rising tuition to students and parents.

Harvard sets aside money for its pension liability every year, as required by law. But it has less than one-third of the money set aside for the medical liability, because these plans are considered pay-as-you-go. Schools have to estimate the total liability, but do not have to set all the money aside in advance.

Yale University, for instance, has a $1.1 billion pension liability, $700 million of which is funded. It has an $820 million retiree medical obligation, but just $274 million of that has been set aside.

Retiree benefits are important because they are part of the packages universities use to compete for talented professors and staff. Many schools have been shifting away from traditional pensions, instead adopting 401(k)-type plans that many corporations use. They feature employee contributions and employer matches. Stanford University, Dartmouth College, and BU have adopted this type of plan, known as a 403(b) in higher education.

The Massachusetts Institute of Technology, in contrast, has the largest pension obligation among its peers, at $2.3 billion. But MIT’s pension is 100 percent funded, because the school has set aside money for the plan for 20 years and invested it in a similar way to its successful endowment. MIT has funded 50 percent of its $472 million retiree medical obligation for 22,000 current and future retirees — a higher percentage than at other schools reviewed by the Globe.

“We have a deep belief of providing a retirement benefit,’’ said MIT’s vice president for finance, Israel Ruiz. “Our mission is driven by a long-term association with faculty, having generous benefits that attract people, so they don’t leave to go elsewhere. I think it’s a crucial factor.’’

Ruiz and other administrators say the large medical-benefit liabilities are manageable — for now. But with people living longer and medical costs continuing to rise rapidly, the projected payouts are likely to accelerate.

Medical benefit liabilities are overtaking pension obligations at universities nationwide, according to Standard & Poor’s, the New York bond analysis firm. In general, the medical benefits “are more of a liability than the pensions,’’ said Mary Peloquin-Dodd, a managing director for higher-education ratings at Standard & Poor’s. That’s in part because of declining pension liabilities, as schools shift away from traditional pensions.

As in government, no one in higher education is eager to reduce benefits for employees. In many cases, less generous plans are being introduced for new hires. But the tradition of generous retirement offerings at universities may be challenged.

“We’ve got to be vigilant of what we’re promising, so we can sustain it,’’ Ruiz said.

If costs keep rising, and people are living into their 90s and longer, he said, “something’s going to have to give.’’